Open clusters with Hipparcos I. Mean astrometric parameters N. Robichon, Frédéric Arenou, J.-C Mermilliod, C. Turon
To cite this version:
N. Robichon, Frédéric Arenou, J.-C Mermilliod, C. Turon. Open clusters with Hipparcos I. Mean astrometric parameters. Astronomy and Astrophysics - A&A, EDP Sciences, 1999, 345 (2), pp.471- 484. hal-02053849
HAL Id: hal-02053849 https://hal.archives-ouvertes.fr/hal-02053849 Submitted on 1 Mar 2019
HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Astron. Astrophys. 345, 471–484 (1999) ASTRONOMY AND ASTROPHYSICS Open clusters with Hipparcos? I. Mean astrometric parameters
N. Robichon1,2, F. Arenou2, J.-C. Mermilliod3, and C. Turon2 1 Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The Netherlands 2 Observatoire de Paris, section de Meudon, DASGAL/CNRS URA 335, F-92195 Meudon CEDEX, France (Noel.Robichon, Frederic.Arenou, [email protected]) 3 Institut d’Astronomie de Lausanne, CH-1290 Chavannes des Bois, Switzerland ([email protected])
Received 9 December 1998 / Accepted 19 February 1999
Abstract. New memberships, mean parallaxes and proper mo- absolute position of the main sequences of several open clusters tions of all 9 open clusters closer than 300 pc (except the Hyades) independently of any preliminary knowledge of the chemical and 9 rich clusters between 300 and 500 pc have been computed composition. According to the present data on chemical compo- using Hipparcos data. Precisions, ranging from 0.2 to 0.5 mas sition, no large discrepancies are found between the Hipparcos for parallaxes and 0.1 to 0.5 mas/yr for proper motions, are of distance moduli of most of the cluster and the positions of their great interest for calibrating photometric parallaxes as well as sequences in the HR diagram (Mermilliod et al. 1997a, Robi- for kinematical studies. Careful investigations of possible biases chon et al. 1997), with the noticeable exception of the Pleiades. have been performed and no evidence of significant systematic Because the Main-Sequence Fitting (MSF) method is still the errors on the mean cluster parallaxes has been found. The dis- basic tool in determining the distances of open clusters, the tances and proper motions of 32 more distant clusters, which understanding of the Pleiades anomaly appears to be the first may be used statistically, are also indicated. priority. Pinsonneault et al. (1998) (herafter PSSKH) have tackled Key words: stars: distances – Galaxy: open clusters and asso- the problem with a grid of models adapted to the mass range ciations: general of solar-type stars which are unevolved in nearby clusters, and chemical composition of these clusters. Their method deter- mines the distance modulus and metallicity simultaneously from 1. Introduction (MV , (B V )0) and (MV , (V I)0), using the fact that (V I) is much less− sensitive to the metallicity− than (B V ). Good− Hipparcos observations of stars in nearby open clusters offer, for agreement is found for several clusters (Hyades,− Praesepe, α the first time, the possibility of determining accurate distances Persei), i.e. the distances determined for the adopted metallic- to these clusters without any assumption about their chemical ity correspond to those obtained from Hipparcos. Problems are composition or about stellar structure. The new distance mod- found for the Pleiades (and Coma Ber cluster which only has ulus of the Hyades, 3.33 0.01, derived by Perryman et al. colours). PSSKH attributed these discrepancies to 1 mas ± B V (1998) is a first step in the determination of the distance scale systematic− errors in the Hipparcos Catalogue. in the universe. The high precision obtained represents an im- In fact, a more general view of the situation should be ob- portant improvement with respect to the results of decades of tained from the analysis of additional nearby open clusters. For attempts to fix the zero point of the distance scale. example, NGC 2516 which occupies the lowest position in the The position of the Zero Age Main Sequence (ZAMS) is HR diagram with respect to Praesepe (even below that of the sensitive to the exact chemical composition of the clusters and Pleiades) has a metallicity [F e/H]= 0.32 (Jeffries et al. a difference of [Fe/H] = 0.15, corresponding to the metallicity 1997), in good agreement with that required− to adequately fit difference between the Hyades and the Sun, results in a dis- the ZAMS in the colour-magnitude diagram. placement of about 0.2 magnitude in absolute magnitude (MV ) The results and detailed discussions presented in this pa- according to several internal structure and atmosphere mod- per are in keeping with preliminary results presented at the els. As the exact chemical composition of most clusters is not Venice’97 Symposium (Robichon et al. 1997). Since this Sym- presently known with the required accuracy, the metallicity cor- posium, careful investigations of possible biases have been per- rections to the distance moduli are not known with precision. formed, but no evidence of any bias larger than few tenths of a Thanks to Hipparcos observations, it is possible to determine the milliarcsecond has been discovered. Discrepancies between the Send offprint requests to:Noel¨ Robichon parallaxes of the Pleiades and Coma Ber with the ground-based ? Based on observations made with the ESA Hipparcos astrometry values of Pinsonneault et al. still exists, and an attempt to ex- satellite plain them will be given in a following paper (Robichon et al. 472 N. Robichon et al.: Open clusters with Hipparcos. I in prep.). This second paper will analyse the cluster sequences can be derived with good accuracy. Because they are quite dif- in the colour-magnitude diagram in the light of Hipparcos data. ferent from field star parallaxes and pro-per motions, a new and It will complete the analysis of the cluster sequences in several secure selection of members in the Hipparcos Catalogue can photometric systems presented in Mermilliod (1998) which ex- be performed, which replaces the pre-launch selected sample. hibits a significant correlation between the cluster metallicities This concerns all the clusters closer than 300 pc and 8 additional and their relative positions in the (MV , (B V )0) diagram clusters closer than 500 pc. when using the Hipparcos distance moduli. − For the other clusters, situated further than 500 pc or with The outline of the paper is the following. Sect. 2 depicts the a number of Hipparcos stars smaller than 8, the mean paral- two different methods adopted for selecting cluster members laxes and proper motions are small or not accurate enough and from the Hipparcos astrometric data, depending on whether or members are harder to separate from field stars on an astromet- not they are closer than 500 pc and contain at least 8 members. ric basis. A selection based only on astrometrical criteria would With these sets of members, the mean astrometric parameters accept non member stars and could then bias the computed mean (π, µα cos δ, µδ) of 18 rich clusters closer than 500 parsecs, and parameters of the cluster. Nevertheless, even if the mean Hip- 32 more distant and/or containing between 4 and 7 members, parcos parallax is not so precise compared to distance modulus are computed and given in Sect. 3. The method used to compute derived, for example, from a MSF, it is interesting to compute these mean astrometric parameters is briefly described. It uti- their mean astrometric parameters for at least two reasons. On lizes Hipparcos intermediate data which allow to take account the one hand, mean parallaxes of dozens of clusters allow statis- of the star to star correlations. The rest of the paper reviews the tical calibration of other distance indicators. On the other hand, possibility of systematic errors in the parameters both at large the cluster mean proper motions can be very useful for galactic scale and small scale. The conclusion of this last part is that the kinematic studies. For these clusters, only stars preselected in mean astrometric parameters are statistically unbiased over the the Hipparcos Input Catalogue were taken into account. For the sky and that their formal errors are not severely underestimated. 110 clusters farther than 300 pc and with at least 2 Hipparcos stars, the mean astrometric parameters have also been derived. 2. Selection of cluster members No attempt has been made to find new nearby clusters in the Hipparcos Catalogue. Platais et al. (1998) made a survey of new 2.1. Pre-launch selection open clusters and associations in the Hipparcos Catalogue. They The initial selection for inclusion of cluster stars in the Hippar- found some possible new clusters which need to be confirmed cos Input Catalogue (HIC) (Turon et al. 1992) is described in by further analysis at fainter stars. These new objects are then detail in (Mermilliod & Turon 1989). It was based on the condi- not included in the present paper. The same goes for OB asso- tions of membership from proper motions and radial velocities ciations which are studied in detail using Hipparcos data in a when available, and the positions in the colour-magnitude di- comprehensive paper by de Zeeuw et al. 1999. The method used agram on the single star sequence to minimize the effects of here to derive cluster mean astrometric parameters is not suited potential companions. Further selections were applied during for the Hyades because its depth is not a negligible fraction of its the mission simulations to remove those stars that could be af- distance at the Hipparcos precision. The Hyades properties were fected by veiling glare of bright neighbouring stars. In the case analysed in detail by Perryman et al. (1998) with the Hipparcos of the Pleiades and Praesepe, stars from the outer region have data. been included in the sample to enlarge the total number of stars The selections carried out in this paper rely on the assump- in these two clusters. As in any other field, the selection was tion that all the cluster members have the same space velocity also constrained by the satellite capabilities and was achieved and, for the closest clusters, that they lie within a 10 parsec radius through simulations. sphere centred on the cluster centre (which roughly corresponds The candidates in the Praesepe and Pleiades clusters were to the tidal radius of an open cluster). One cluster, NGC 1977, selected on the basis of proper motion, radial velocity and pho- has been rejected from the present study because the distribu- tometry analysed in Mermilliod et al. (1990) and Rosvick et al. tion of its members over the sky is not in good agreement with (1992), with the same criteria, especially concerning the duplic- a bound cluster (in particular, no centre can be defined). These ity. These conditions are reflected in the fact that the sequences stars are rather part of a 80 pc long feature, connected with the in the colour-magnitude diagrams of most clusters are quite nar- Orion OB1 association (Tian et al. 1996). Another nearby object, row. Melotte 227, as well as most of the nearby Collinder groups (Cr 399, 359, 135 and 463) have been rejected since the astrometric data of the preselected stars do not show the characteristics of 2.2. Final catalogue member selection an open cluster, in particular in their spatial structure. In this study, two different member selections have been applied to the open clusters in order to securely distinguish the members 2.2.1. Members in the closest clusters from the field stars based on their astrometric parameters (π, µα cos δ, µδ). Although a visual examination of the vector-point and colour- The mean astrometric parameters of clusters closer than magnitude diagrams can easily confirm the presence of an open 500 pc and containing at least 8 stars observed by Hipparcos cluster, an objective selection of members is always an issue. N. Robichon et al.: Open clusters with Hipparcos. I 473
Table1. Equatorial coordinates (J2000.0) from Lynga˚ (1987) and mean cos measured the brightest and thus bluest part of the main se- radial velocity of the cluster centres quence, there are few stars in common between the CORAVEL and HIPPARCOS samples for most of the clusters. Therefore, Cluster αδ VR # of@ CORAVEL mean velocities have been computed from all ob- ◦0 − name h m s km s 1 stars served known members (not only Hipparcos members), with Coma Ber 12 25 07 26 06.6 -0.1 ± 0.2 22(1) the exclusion of binaries without a determination of orbital el- Pleiades 3 47 00 24 03.0 5.7 ± 0.5 78(1) ements. When too few CORAVEL data were available, radial IC 2391 8 40 14 -53 03.6 14.1 ± 0.2 15(1) velocities from the WEB Catalogue (Duflot et al. 1995) of the IC 2602 10 43 12 -64 24.0 16.2 ± 0.3 18(1) Hipparcos stars selected in this paper were averaged. Fortu- ∗ Praesepe 8 40 00 19 30.0 34.5 ± 0.0 104(1) nately, the value of the mean cluster radial velocities does not NGC 2451 7 45 12 -37 58.2 28.9 ± 0.7 5(2) need to be so precise since only its projection at the position of −1 α Per 3 22 02 48 36.0 -0.2 ± 0.5 18(1) each member is used. For example, an error of 1 km s in the Blanco 1 0 04 24 -29 56.4 5.1 ± 0.2 28(1) mean radial velocity would induce an error on the proper mo- NGC 6475 17 53 43 -34 48.6 -14.7 ± 0.2 40(1) tion of a Pleiades member situated at 3 degrees from the cluster NGC 7092 21 32 12 48 26.4 -5.4 ± 0.4 7(1) centre (6 pc) of about 0.1 mas/yr. Mean radial velocities and the NGC 2232 6 26 24 -4 45.0 21.0 ± 0.6 4(2) number of stars and references of the sources (Coravel or the IC 4756 18 38 58 -5 27.0 25.8 ± 0.2 13(1) WEB Catalogue) used to compute them are given in Table 1. NGC 2516 7 58 00 -60 48.0 22.7 ± 0.4 6(2) Each star in the area of the cluster is submitted to a suc- Trumpler 10 8 47 48 -42 29.4 25.0 ± 3.5 2(2) cession of selection tests described hereafter and taking into NGC 3532 11 06 24 -58 42.0 3.1 ± 2.5 3(2) account its position, parallax, proper motion and photometry, Collinder 140 7 23 55 -32 12.0 19.9 ± 3.1 4(2) their associated errors, and the mean radial velocity of the clus- NGC 2547 8 10 48 -49 18.0 14.4 ± 1.2 5(2) ter. NGC 2422 7 36 36 -14 30.0 29.4 ± 3.7 4(2) x Let i =(πi,µαi cos δi,µδi) be the vector containing the Σ Source of the mean radial velocity: Hipparcos parallax and proper motion of star i with i being (1) CORAVEL mean value of members selected from CORAVEL and the covariance matrix. Let x0 =(π0,µα0 cos δ0,µδ0) be the photometric data; parallax and proper motion of the cluster centre corresponding (2) mean value from the WEB Catalogue (Duflot et al. 1995) of selected to the mean velocity of the cluster with covariance matrix Σ0. Hipparcos members. Let x0 =(π0,µ 0 cos δ ,µ 0 ) be the parallax and proper ∗ i α i i δ i coordinates from Raboud & Mermilliod 1998. motion corresponding to the mean velocity of the cluster at the the last column indicates the number of members used to compute the position of star i with covariance matrix Σ0i. These are deduced mean radial velocity. from x0 and Σ0 and the mean radial velocity of the cluster VR0 by the following rotation: The selection presented in this section is based on an iterative µ 0 cos δ = cos ∆α µ 0 cos δ0 method, which converges after 2 or 3 iterations, namely when α i i i α no more stars are rejected from the selection. This iterative pro- +sin δ0 sin ∆αiµδ0 cedure is primed with a set of well known members. VR0π0 cos δ0 sin ∆αi (1) At each iteration, the cluster mean parallax and mean proper − 4.74 motion at the position of the centre are computed from Hippar- µδ0i = sin δi sin ∆αiµα0 cos δ0 cos intermediate data, according to the computation described − +(cos δi cos δ0 + sin δi sin δ0 cos ∆αi)µδ0 in Sect. 3, using the members selected at the previous iteration. VR0π0 The computation also takes into account the cluster mean radial +(cos δi sin δ0 sin δi cos δ0 cos ∆αi) − 4.74 velocity to correct the perspective effect due to the different angular directions of the members compared to the cluster cen- where (αi,δi) are the equatorial coordinates of star i, (α0,δ0) tre. The values of cluster centres are taken from Lynga˚ (1987) are the equatorial coordinates of the cluster centre and ∆αi = except for the Pleiades for which it is taken from Raboud & αi α0. Note that, since the cluster depth is neglected, all the − Mermilliod (1998) who derived a new centre of mass for the members are assumed to share the same parallax π0. cluster. These cluster centres are fixed once for all and are not Assuming a Gaussian distribution of errors, the value χ2 = T −1 calculated from Hipparcos data since the number of Hipparcos (xi x0i) (Σi + Σ0i) (xi x0i) follows a Chi-square stars in each cluster is generally not large enough to obtain new distribution− with 3 degrees of freedom.− Star i is considered as a accurate cluster mass centres. cluster member if χ2 < 14.16 (corresponding to a 3σ Gaussian When available, radial velocities obtained with the CORA- two-sided test). VEL radial-velocity scanner by Rosvick et al. (1992), Mermil- If star i is considered as a cluster member at the previous liod et al. (1997b) and additional unpublished data have been iteration, i.e. if it is used for the calculation of Σ0i, then Σi and used to compute cluster mean radial velocities VR0. Σ0i are correlated. Nevertheless this correlation is small and Because the CORAVEL scanner is adapted to measure stars has been neglected because Σ0i is calculated with a sufficiently later than the spectral type F5 (B V>0.45) while Hippar- large number of stars (between 8 and 54). − 474 N. Robichon et al.: Open clusters with Hipparcos. I
A diagonal correlation matrix simulating the depth of the below). They may be useful mainly for statistical studies (e.g. cluster and the internal velocity dispersion can be added to Σi Sect. 4.2.2). and Σ0i but it is small compared to them. For example, using 2 pc as a typical cluster core radius and a velocity dispersion of 0.5 km s−1, the member selection in each cluster remains unchanged. 3. Cluster mean astrometric parameters To avoid any erroneous selection, stars with a standard er- ror of the parallax larger than 3 mas or a standard error of the 3.1. Hipparcos intermediate data proper motion larger than 3 mas/yr have also been rejected. This The mean cluster parallax cannot be computed without caution concerns only 1 or 2 stars per cluster at the most. from the Hipparcos observations. As was explained before the To be sure that only real members are selected, and not stars satellite launch, the estimation of the mean parallax or proper from a possible moving group associated with the cluster, stars motion of a cluster observed by Hipparcos must take into ac- whose distance from the cluster centre, perpendicularly to the count the observation mode of the satellite (Lindegren 1988). line of sight, is greater than 10 pc (corresponding to a typical This is due to the fact that stars within a small area in the sky open cluster tidal radius) have also been rejected. have frequently been observed in the same field of view of the Hipparcos double stars were rejected when their duplicity satellite. Consequently, one may expect correlations between could damage or bias the mean proper-motion and parallax val- measurements done on stars separated by a few degrees, or with ues, i.e. when the field H59 of the Hipparcos Catalogue was a separation being a multiple of the basic angle (58◦) between equal to C, G, O, V or X (see ESA 1997). G, X and V entries the two fields of view. have abscissae on the Reference Great Circles (RGC) which The consequence is that, when averaging the parallaxes or reflect the combination of the proper motion of the system (de- proper motions for n stars, the improvement factor does not pending of the mean cluster velocity) and the orbital motion follow the expected 1/√n law and will not be asymptotically of the system. C and O entries have a proper motion in the better than √ρ if ρ is the mean positive correlation between Hipparcos main Catalogue decoupled from the orbital motion data (Lindegren 1988). Ignoring these correlations would thus because they were reduced with an appropriate algorithm taking underestimate the formal error on the average parallax. into account more than the 5 astrometric parameters needed to The proper way to take these correlations into account is to describe the astrometry of a single star. The global cluster re- go one step back in the Hipparcos reduction and to work with duction (Sect. 3) doesn’t take these supplementary parameters the abscissae of stars on the Reference Great Circles (RGC), into account and thus, the astrometric parameters that are cal- as observed by the satellite. Then, by calibrating the correla- culated for these stars could be biased by the orbital motions. tions between the RGC abscissae, the full covariance matrix V Hipparcos double stars considered as cluster members and not between observations allows to find the optimal astrometric pa- used in the reduction are given in the appendix Table A1. rameters. The method, fully described in van Leeuwen & Evans Once cluster members have been selected from their astro- (1998), has been used with minor differences only. The calibra- metric parameters, their membership is verified with the help tion of correlation coefficients has been done on each RGC, the of the (V,B V ) colour-magnitude diagram (hereafter CMD). reason being that significant variations may be found from one − This test was positive for all clusters, except for NGC 6475 in orbit to another (Arenou 1997). This has been done using the which two stars (HIP 86802 and 88224) were rejected according theoretical formulae of Lindegren (1988) to which harmonics to their discrepant positions in the CMD. were added through the use of cosine transform (Press et al. The cluster members obtained by this selection process are 1992). Another difference from van Leeuwen & Evans (1998) listed (by HIP number) in the appendix Table A2. The number comes from the fact that the formal abscissae errors and cor- of selected members varies from 8 to 54. relations have been recalibrated as described in Arenou (1997) using the final Hipparcos data, the changes being at the level of few percent only. 2.2.2. Selection of members in more distant clusters The quantities of interest are the mean parallax π0 and the mean proper motion µα0 cos δ0, µδ0 of each cluster centre and For the most distant clusters or for clusters with less than 8 the position αi,δi of each cluster member i. When computing members, the selection is more difficult. Because it is not possi- the cluster mean parallax, one implicitly assumes that the dis- ble to redefine a secure membership selection for these clusters, persion in individual parallaxes is only due to the measurements only the HIC preselected stars were taken into account and no errors. In fact, the depth of the cluster increases the error on the attempt has been done to identify new members. Possible non- mean cluster parallaxes by few tenths of mas but should not bias members were excluded using BDA, the open cluster database it under the hypothesis that stars are symmetrically distributed. (Mermilliod 1995). An iterative procedure was then applied to In the Hipparcos intermediate data CD-ROM, the abscissae compute the mean proper motion of the members and to reject are not given but their residuals with respect to the main Hip- stars with a proper motion discrepant by more than 3σ from parcos Catalogue astrometric parameters are given instead. The the mean. The final mean astrometric parameters are then com- new residuals on the abscissae, δa, with respect to the current puted in the same way as for the nearby clusters (see Sect. 3 iteration value of (αi, δi, π0, µα0 cos δ0, µδ0) are computed. The N. Robichon et al.: Open clusters with Hipparcos. I 475 corrections to these parameters δpk are then found by weighted parallaxes, the photometric parallaxes are far more precise. We least-squares, minimizing could have derived the mean proper motion simultaneously with T the parallax, but it was prefered to constrain the parallax to its 5 a 5 a ∂ −1 ∂ photometric estimate and to compute the resulting mean proper δa δpk V δa δpk . − ∂pk − ∂pk k=1 ! k=1 ! motion (Table 4). In general, these proper motions are close to X X those obtained without adopting the photometric parallax, but ∂ai ∂ai Using the partial derivatives cos , of the star i ∂µαi δi ∂µδi this allows to gain one degree of freedom. given in the Hipparcos intermediate astrometric data annex, the partial derivatives of the abscissae with respect to the mean proper motion (µ 0 cos δ0,µ 0) are thus computed using the α δ 4. Systematic errors linear equations 1 and the relations ∂a ∂a ∂π ∂a ∂µ cos δ ∂a ∂µ 4.1. Systematics in the Hipparcos Catalogue i = i i + i αi i + i δi 0 0 0 0 ∂π ∂πi ∂π ∂µαi cos δi ∂π ∂µδi ∂π For the Hipparcos mission, the question of systematic errors has
∂ai ∂ai ∂µαi cos δi ∂ai ∂µδi always been a major issue; it should be remembered that, apart = + ∂µα0 cos δ0 ∂µαi cos δi ∂µα0 cos δ0 ∂µδi ∂µα0 cos δ0 from the higher number of stars measured, one of the advan- tages of the Hipparcos data over the ground-based parallaxes ∂ai ∂ai ∂µαi cos δi ∂ai ∂µδi = + is the uniformity of global astrometry observed by a single in- ∂µδ0 ∂µαi cos δi ∂µδ0 ∂µδi ∂µδ0 strument. Therefore, during the data reduction special attention As part of the least-square procedure, the final covariance was paid in order to keep the systematics far below the random matrix between all the astrometric parameters is also computed. errors. A recent study (Makarov, 1998, priv. comm.) shows that systematic intra-revolution variations of the basic angle or of the star abscissae, of the order of 4 mas through the entire mis- 3.2. Results sion, would be needed in order to produce a 1 mas systematic The mean astrometric parameters (π, µα cos δ, µδ) and associ- error of the parallaxes in the Pleiades area. If this had occurred, ated standard errors of clusters closer than 500 pc are given in it would have produced sizable distortions in other parts of the Table 2. The unit weights errors are close to 1 but, in general, sky, and consequently a scatter in parallax measurements much slightly smaller. This is possibly because the star to star corre- greater than predicted by the formal errors. lations between abscissae on the RGCs have not been perfectly The accuracy and formal precision of the Hipparcos data calibrated. However this also suggests that non members have has been verified before the delivery of the data (Arenou et not been erroneously included and that the cluster depth did not al., 1995, 1997, Lindegren 1995). Among the available external play a significant role. data of better or comparable precision, the comparisons used The derived distance parameters (distances and distance the best ground-based parallaxes, distant stars, distant clusters moduli) given in Table 2 deserve some further comments. Since and Magellanic Cloud stars. In the two latter cases, it should be the transformation from parallax to distance or absolute magni- pointed out that these comparisons gave some insight into the tude is not linear, a small bias could be expected (see Brown et property of the parallax errors at small angular scale, although al. 1997). However, the relative error σπ/π is small (between 2 the effect of astrometric correlations was taken into account only and 20 percent) so the effect is negligible (between 0.04 percent approximately. In all cases, it was shown that, over the whole and 4 percent). catalogue, not only the zero-point was smaller than 0.1 mas, Table 3 shows the derived kinematical parameters (U, but also that the formal errors were not underestimated by more V , W ) of clusters. They are computed using a solar motion than 10%, this slight underestimation being possibly due to (U ,V ,W ) = (10.00, 5.25, 7.17) km s−1 (Dehnen & Bin- undetected≈ binaries. In any case, this is far from the 60% ney 1998), with respect to the LSR. which would be needed for the brighter stars to have≈ 1 mas Concerning the more distant clusters, the mean cluster par- systematic errors. allaxes have been computed as described above, under the stan- However, the statement of PSSKH that small-scale system- dard assumption that members of a given cluster share the com- atic errors may be present in Hipparcos data is not unjustified. mon parallax and proper motion. This concerns 110 clusters Indeed, in a given cluster, the afore mentioned correlations be- more distant than 300 pc with at least 2 Hipparcos stars (among tween abscissae may be considered as a small error shared by the which 9 clusters described in Table 2). The parameters of 32 of stars within a few square degrees. These errors, probably ran- these clusters containing at least 4 stars observed by Hipparcos domly distributed over the sky, may thus be regarded as system- are indicated Table 4. The parameters of the remaining clus- atics at small-scale. However, the method outlined in Sect. 3.1 ters are not given here though part of them are included in the takes these correlations into account during the computation of comparison of parallaxes between Hipparcos and groundbased the mean parallax and its associated precision. Then the ques- determinations in Sect. 4.2.2. tion is whether the mean cluster distances and their formal errors Since the relative parallax error of these distant clusters is appear statistically biased. The following sections will answer 40% on the average, their mean parallaxes are not useful in- in the negative using comparisons with previous determinations dividually, but rather for statistical studies. Compared to these of cluster parallaxes and with the help of ad hoc simulations. 476 N. Robichon et al.: Open clusters with Hipparcos. I
Table 2. Cluster mean astrometric parameters.
Cluster NS uwe πµα cos δµδ d (pc) (M − m)0 name NA NR σπ σµα cos δ σµδ ρµα cos δ ρµδ ρµδ π π µα cos δ +1.6 +0.04 Coma Ber 30 0.97 11.49 -11.38 -9.05 87.0−1.6 4.70−0.04 1563 15 0.21 0.23 0.12 -0.13 0.06 -0.12 +3.2 +0.06 Pleiades 54 0.98 8.46 19.15 -45.72 118.2−3.0 5.36−0.06 2158 25 0.22 0.23 0.18 -0.16 -0.07 0.21 +4.8 +0.07 IC 2391 11 0.94 6.85 -25.06 22.73 146.0−4.5 5.82−0.07 807 4 0.22 0.25 0.22 0.05 0.07 0.22 +3.8 +0.05 IC 2602 23 0.93 6.58 -17.31 11.05 152.0−3.6 5.91−0.05 1766 13 0.16 0.16 0.15 0.08 0.10 0.21 +10.7 +0.13 Praesepe 26 1.03 5.54 -36.24 -12.88 180.5−9.6 6.28−0.12 1126 6 0.31 0.35 0.24 -0.22 -0.11 -0.15 +7.0 +0.08 NGC 2451 12 0.92 5.31 -22.14 15.15 188.7−6.5 6.38−0.08 908 7 0.19 0.16 0.19 0.03 0.03 -0.03 +7.2 +0.08 α Per 46 0.94 5.25 22.93 -25.56 190.5−6.7 6.40−0.08 2198 12 0.19 0.15 0.17 0.14 -0.01 0.37 +34.3 +0.27 Blanco 1 13 0.96 3.81 19.15 3.21 262.5−27.2 7.10−0.24 798 10 0.44 0.50 0.27 0.26 0.05 -0.21 +25.7 +0.19 NGC 6475 22 0.82 3.57 2.59 -4.98 280.1−21.7 7.24−0.18 772 3 0.30 0.34 0.21 -0.10 0.04 -0.12 +30.7 +0.20 NGC 7092 8 0.92 3.22 -7.79 -19.70 310.6−25.7 7.46−0.19 589 1 0.29 0.29 0.25 -0.07 0.03 -0.18 +41.6 +0.26 NGC 2232 10 0.91 3.08 -4.67 -3.08 324.7−33.1 7.56−0.23 497 2 0.35 0.30 0.26 -0.07 0.03 0.05 +59.1 +0.36 IC 4756 9 0.99 3.03 -0.52 -5.83 330.0−43.5 7.59−0.31 522 1 0.46 0.40 0.33 0.07 0.10 0.00 +27.1 +0.16 NGC 2516 14 0.92 2.89 -4.04 10.95 346.0−23.4 7.70−0.15 947 4 0.21 0.22 0.20 0.10 0.05 -0.13 +43.2 +0.24 Trumpler 10 9 0.97 2.74 -13.29 7.32 365.0−34.9 7.81−0.22 702 2 0.29 0.25 0.24 0.04 0.06 0.03 +75.9 +0.37 NGC 3532 8 0.92 2.47 -10.84 5.26 404.9−55.2 8.04−0.32 552 5 0.39 0.38 0.37 -0.01 0.06 0.42 +55.3 +0.27 Collinder 140 11 0.97 2.44 -8.52 4.60 409.8−43.5 8.06−0.24 911 2 0.29 0.22 0.28 0.06 0.09 0.07 +62.1 +0.29 NGC 2547 11 0.95 2.31 -9.28 4.41 432.9−48.3 8.18−0.26 824 3 0.29 0.31 0.24 0.10 0.15 0.06 +135.4 +0.52 NGC 2422 9 0.97 2.01 -7.09 1.90 497.5−87.7 8.48−0.42 591 1 0.43 0.35 0.28 -0.13 -0.04 0.43
π and σπ are in mas, µα cos δ, µδ, σµα cos δ and σµδ are in mas/yr. The notations have the following meaning: NS: number of Hipparcos stars used for the calculation, NA: number of accepted abscissae, NR: number of rejected abscissae, uwe: unit-weight error. N. Robichon et al.: Open clusters with Hipparcos. I 477
Table 3. Cluster mean derived kinematical parameters. The velocity takes the solar motion (10.00,5.25,7.17) km s−1 into account, but not the rotation of the LSR
U V W V W W Cluster lbUσU VσV WσW ρπ ρπ ρπ ρU ρU ρV name degree km s−1 percent Coma Ber 221.28 84.03 7.82 0.09 -0.31 0.12 6.62 0.25 29 84 4 48 -16 -10 Pleiades 166.62 -23.57 3.65 0.45 -19.12 0.69 -5.85 0.35 99875-56064 IC 2391 270.36 -6.89 -12.92 0.75 -8.33 0.25 1.18 0.24 98 -5 64 -6 64 2 IC 2602 289.63 -4.89 1.56 0.37 -15.01 0.30 6.88 0.12 93 41 -10 17 -10 13 Praesepe 206.07 32.34 -32.43 0.88 -14.99 0.44 -2.02 1.51 98 90 99 82 99 88 NGC 2451 252.40 -6.75 -18.74 0.80 -14.43 0.73 -6.79 0.44 94 -40 92 -15 90 -20 α Per 146.96 -7.12 -5.32 0.69 -20.53 0.96 -0.70 0.35 80 96 85 61 77 77 Blanco 1 14.95 -79.30 -11.68 2.51 -1.78 0.90 -2.35 0.54 98 87 91 90 92 85 NGC 6475 355.84 -4.49 -5.36 0.20 2.37 0.44 2.04 0.71 33 72 80 25 32 42 NGC 7092 92.46 -2.28 38.37 2.55 0.50 0.42 -6.05 1.31 -99 -14 94 14 -93 -13 NGC 2232 214.33 -7.73 -5.67 0.57 -6.66 0.48 -4.13 1.05 -32 9 90 31 -25 8 IC 4756 36.38 5.25 35.99 0.91 13.83 1.16 6.16 0.78 -93 92 64 -97 -58 52 NGC 2516 273.86 -15.89 -7.43 1.42 -18.48 0.42 3.30 0.36 97 31 -36 29 -32 -2 Trumpler 10 262.82 0.63 -17.25 2.65 -16.62 4.97 -2.48 1.16 96 -6 93 17 88 -10 NGC 3532 289.64 1.43 -10.92 3.56 -4.84 2.66 8.32 0.83 96 46 -16 24 -9 -11 Collinder 140 245.20 -7.85 -11.79 2.65 -4.91 4.59 -6.10 1.54 59 -20 84 64 83 26 NGC 2547 264.60 -8.55 -8.90 2.24 -5.58 1.26 -6.15 1.62 97 -34 92 -30 92 -24 NGC 2422 230.98 3.13 -18.26 3.14 -10.50 3.25 -3.65 2.71 66 -46 94 34 57 -49
4.2. Comparison with previous determinations Focusing on the 7 nearest clusters for which the Hipparcos distance modulus errors are smaller than 0.1 magnitude (and The first checking of the mean parallaxes comes from compar- excluding NGC 2451 for the reasons given below), the following ison with previous determinations. The first part of this section remarks can be done: mainly deals with the 7 closest clusters, which have a formal error on the Hipparcos distance modulus smaller than 0.1 mag- – Coma Ber and α Per distance moduli are larger for Hip- nitude and can thus be compared individually with other deter- parcos than for the other references. Concerning α Per, it minations. The second part analyses statistically the parallaxes should be noticed that the difference between Hipparcos of the clusters more distant than 300 parsecs. and PSSKH, 0.17 magnitude, is nearly twice as small as the difference between PSSKH and Dambis, 0.30 magnitude. 4.2.1. The closest clusters – The Pleiades distance modulus is smaller for Hipparcos, but the difference between Dambis and Hipparcos, 0.11 magni- Previous cluster distance determinations were mainly derived tude, is in the order of the difference between PSSKH and from the MSF technique. With the exception of the Hyades, Dambis, 0.13 magnitude. where ground-based trigonometric parallaxes are in excellent – IC 2391 and 2602 are approximatively at the same distance agreement with the Hipparcos ones (see Perryman et al. 1998), for Dambis, Loktin & Matkin and Hipparcos, but the Hip- and the series of papers by Gatewood et al. (1990), Gatewood parcos value is between the two others which are discrepant & Kiewiet de Jonge (1994) and Gatewood (1995) (see below), by 0.35 magnitude (0.25 if Loktin & Matkin are corrected practically no direct determination of distance exists in the lit- from the distance modulus of the Hyades). erature. Distance moduli of the 18 clusters derived from the Hippar- No systematic differences are, thus, noticeable between Hip- cos mean parallaxes are compared in Table 5 to those determined parcos distance moduli and ground-based ones in the sense that by Lynga˚ (1987), Dambis (1999), Loktin & Matkin (1994) and there is no general trend of the Hipparcos distance moduli to be Pinsonneault et al. (1998). Lynga’s˚ values, though outdated, are different from all the MSF distance moduli from all the cited given for comparison, since Lynga’s˚ catalogue of open clus- references. On the contrary, the difference between Hipparcos ter parameters has long been the catalogue of reference. These and any of these references is of the same order, 0.2 magni- values are the result of a compilation and do not present any tude, than that between two of these external references. This homogeneity. On the contrary, Loktin & Matkin (330 clusters) behaviour tends to show that the formal errors of distance mod- and Dambis (202 clusters) catalogues are quite homogeneous. uli derived from the MSF technique are underestimated. This is Because the Hipparcos mean distance modulus of the Hyades not so surprising since MSF distance moduli depend on the the- is 3.33 0.1 (Perryman et al. 1998), the distance moduli of oretical (or empirical) sequence used, the metallicity and the re- ± Loktin & Matkin (1994), which are based on a value of 3.42, denning chosen and the relations used to transform (Teff , Mbol) are probably systematically overestimated by about 0.1 mag. into observable quantities. For example, an error of 0.1 dex in the metallicity will lead to a variation of the distance modulus 478 N. Robichon et al.: Open clusters with Hipparcos. I
Table 4. Mean parameters for all clusters with more than 4 Hipparcos 1998 and Carrier et al. (1998). According to Roser¨ & Bastian members (#) and more distant than 500 pc or with less than 8 Hipparcos NGC 2451 can be divided into two different entities. The closest members. The proper motions have been computed constraining the one, at about 220 pc, has a well defined sequence in the colour- photometric distance estimate πP. This estimate is indicated with its magnitude diagram but presents a large scatter in proper motion reference: D for Dambis, L for Loktin & Matkin, G for Lynga,˚ in as taken from the PPM catalogue and looks more like a moving decreasing order of preference. The units are mas for the parallaxes, group than like an open cluster. The most distant entity, situated mas/yr for proper motions; the correlation coefficient (%) between at about 400 pc, seems to form an open cluster. Platais et al. µ and µ is indicated in the last column. α cos δ δ (1996) definitively found two clusters NGC 2451-a and NGC 2451-b at 190 and 400 pc utilizing CCD photometry, while Car- Name # ππµα cos δµρ P δ rier et al. (1998) confirmed the existence of these two clusters mas mas mas/yr % at 198 and 358 pc from Geneva photometry and the Hipparcos Cr 121 13 1.80±.24 1.58D -3.88±.16 4.35±.19 19 data. Baumgardt (1998) also found NGC 2451-a at 190 pc from Cr 132 8 1.54±.33 2.43G -3.57±.24 4.16±.31 14 Hipparcos data and supported the existence of NGC 2451-b in ± ± ± IC 1805 4 1.80 .78 0.52D -1.14 .71 -2.29 .62 -32 Hipparcos and ACT data. Using Hipparcos data alone, NGC IC 2944 4 0.56±.43 0.48D -5.61±.38 0.98±.37 11 2451-a (π=5.30 mas) exhibits a distinct clump in the vector- NGC 0457 4 1.55±.58 0.41D -1.49±.40 -1.98±.36 -39 point diagram and a well defined peak in parallax, and has then NGC 0869 4 1.01±.48 0.54D -0.79±.38 -1.44±.33 -25 all the characteristics of an open cluster. Another peak in the par- NGC 0884 5 0.93±.51 0.50D -0.77±.42 -1.87±.35 -31 NGC 1647 4 1.09±.80 2.42D -0.56±.94 -0.14±.77 71 allax distribution at 2.5 mas, corresponding probably to NGC NGC 2244 6 1.37±.56 0.70D -0.59±.46 0.55±.38 -12 2451-b, connected with a concentration in the vector point dia- NGC 2264 6 2.86±.63 1.39D -0.40±.64 -4.05±.44 27 gram near (µα cos δ, µδ)=(-9, 5) is noticeable. But it is difficult NGC 2281 4 0.82±.73 1.89L -2.84±.82 -7.51±.54 17 to distinguish from the field star distribution because both par- NGC 2287 8 1.91±.52 1.53L -4.29±.43 0.04±.44 1 allax and proper motion are close to those of field stars. NGC 2467 5 1.79±.65 0.79D -3.19±.35 1.92±.46 -5 Pleiades, Praesepe and Coma trigonometric parallaxes were NGC 2527 4 1.51±.95 1.65L -6.27±.49 8.14±.69 11 obtained from the ground by Gatewood et al. (1990), Gatewood ± ± ± NGC 2548 5 1.51 .79 1.51L -0.63 .67 0.92 .63 -25 & Kiewiet de Jonge 1994) and Gatewood (1995). In Praesepe, NGC 3114 6 1.14±.36 1.05D -7.77±.39 4.15±.31 -9 the mean parallax from Gatewood (1994) is 5.21 0.8 mas in NGC 3228 4 1.39±.50 1.89L -15.28±.43 0.40±.37 -9 good agreement with Hipparcos and MSF values± of Loktin & NGC 3766 4 1.36±.63 0.59D -7.28±.54 1.19±.52 28 Matkin (1994) and Pinsonneault et al. (1998). For the Pleiades, NGC 4755 5 0.52±.40 0.53D -4.69±.33 -1.47±.30 36 ± ± ± Gatewood et al. (1990) obtained a mean value of 6.6 0.8 mas, NGC 5662 5 1.94 .62 1.39D -5.70 .56 -7.58 .55 -5 ± NGC 6025 4 0.76±.55 1.79D -3.63±.47 -2.87±.53 -28 using 5 cluster members. This value is noticeably smaller than NGC 6087 4 1.30±.61 1.23D -1.60±.62 -1.43±.56 -10 both Hipparcos and MSF values. On the contrary their Coma NGC 6124 4 2.71±.86 2.15L -1.21±.96 -1.92±.71 -31 parallax (Gatewood et al. 1995), 13.53 0.54 mas, is much ± NGC 6231 6 -0.62±.48 0.71D 0.04±.47 -1.94±.34 -18 larger. These discrepancies may be due to the fact that, although NGC 6405 4 1.69±.52 2.19D -1.47±.58 -6.78±.36 -28 the internal accuracy of parallaxes are of the order of 1 mas, the NGC 6530 4 1.31±.80 0.79D 1.26±.86 -2.04±.55 -54 zero point, fixed by 4 field stars for the Pleiades, 6 for Praesepe ± ± ± NGC 6633 4 2.70 .70 2.61L -0.09 .60 -0.39 .51 7 and 8 for Coma, may be uncertain. There is only one field star in NGC 6882 4 2.38±.44 1.68G 2.60±.28 -9.81±.27 -26 common with their list, AO 1143 (=HIP 60233). It has a parallax NGC 7063 4 2.21±.81 1.31L 0.43±.52 -4.24±.56 -20 of 2.3 0.6 in Gatewood et al. (1995) and of 4.27 0.92 mas NGC 7243 4 0.43±.61 1.30D 1.72±.48 -2.41±.52 9 in the Hipparcos± Catalogue. ± Stock 02 5 2.90±.60 3.30G 15.97±.75 -13.56±.54 -42 Tr 37 6 1.03±.38 1.23D -3.75±.35 -3.48±.33 23 Van Leeuwen & Evans (1998) also calculated the mean as- trometric parameters of the Pleiades and Praesepe as an exam- ple of the use of Hipparcos intermediate astrometric data. Their of the order of 0.1 magnitude when using Johnson B,V pho- method is very similar to the one presented in this paper as tometry. And an error of 0.01 magnitude in the reddening will mentioned in Sect. 3.1. The final obtained values (van Leeuwen produce an error of about 0.05 magnitude in m M. 1999), are also close to the ones calculated in this paper. This is Noticing these discrepancies between the− MSF distance not unexpected since the same abscissae have been used in both moduli, it would be prudent to consider the Hipparcos data as cases. However different sets of members and slight differences a good test of the accuracy of MSF, when the exact chemical in the abscissae formal errors and correlations account for the composition of the clusters is not known, and would possibly observed differences in the results. be a way to give constraints on this composition. A review of O’Dell et al. (1994), used the apparent star diameters to the consequences of Hipparcos distance moduli on the MSF derive the distances of the Pleiades and α Per. They obtained technique will be given in the second paper (Robichon et al. in a distance of 132 10 pc for the Pleiades and 187 11 pc for ± ± prep.). α Per. The value of α Per agrees closely with the Hipparcos NGC 2451 presents the most discrepant values. The na- value while the distance of the Pleiades is in agreement with ture of this cluster was already discussed by Roser¨ & Bastian Hipparcos within the error bars. The method makes a statistical (1994) and more recently by Platais et al. (1996), Baumgardt use of V sin i of cluster members associated with their rotational N. Robichon et al.: Open clusters with Hipparcos. I 479
Table 5. Hipparcos compared to previous determinations of cluster distance moduli and redennings.
Cluster (m − M)0 (m − M)0 E(B − V )(m − M)0 E(B − V )(m − M)0 E(B − V )(m − M)0 name Hipparcos Lynga˚ Dambis Loktin & Matkin Pinsonneault et al. +0.04 ∗ Coma Ber 4.70−0.04 4.49 0.00 4.60 0.01 4.54±0.04 +0.06 Pleiades 5.36−0.06 5.48 0.04 5.47±0.05 0.040 5.50 0.04 5.60±0.04 +0.07 IC 2391 5.82−0.07 5.92 0.01 5.74±0.07 0.004 6.07 0.01 +0.05 IC 2602 5.91−0.05 5.89 0.04 5.68±0.05 0.038 6.07 0.05 +0.13 Praesepe 6.28−0.12 5.99 0.00 6.26 0.02 6.16±0.05 +0.08 NGC 2451 6.38−0.08 7.49 0.04 6.92 0.04 +0.08 α Per 6.40−0.08 6.07 0.09v 5.94±0.05 0.099 6.15 0.09 6.23±0.06 +0.27 Blanco 1 7.10−0.24 6.90 0.02 +0.19 NGC 6475 7.24−0.18 6.89 0.06 +0.20 NGC 7092 7.46−0.19 7.33 0.02 7.71 0.01 +0.26 NGC 2232 7.56−0.23 7.80 0.01 7.90±0.05 0.021 7.50 0.03 +0.36 IC 4756 7.59−0.31 7.94 0.20v 8.41 0.20 +0.16 NGC 2516 7.70−0.15 8.07 0.13 7.85±0.05 0.111 7.86 0.10 +0.24 Trumpler 10 7.81−0.22 8.09 0.06 7.80±0.05 0.035 7.64 0.02 +0.37 NGC 3532 8.04−0.32 8.40 0.04 8.23 0.04 +0.27 Collinder 140 8.06−0.24 7.39 0.04 7.71±0.05 0.026 7.70 0.04 +0.29 NGC 2547 8.18−0.26 8.20 0.05 7.90±0.10 0.054 8.16 0.04 +0.52 NGC 2422 8.48−0.42 8.37 0.08 8.13±0.05 0.088 8.15 0.07 ∗ based only on the sequence in the (MV ,B− V ) diagram. v: variable redenning. periods and their angular diameters. Unfortunately, as too few Narayanan & Gould (1999) used the gradient of radial ve- direct angular star diameters are available for Pleiades members, locities to derive a Pleiades mean distance of 130.7 11.1 pc, a calibration of the diameters as a function of V and B V from in agreement with Hipparcos within the error bars. Their± set of Hendry et al. (1993) was used. As for the MSF method,− these 154 individual radial velocities is a compilation of CORAVEL distances are thus not directly obtained but, once again, they measurements taken from the same references as those of depend on calibrations which can be biased by several other Sect. 2. They used a mean proper motion of (µα cos δ, µδ)= parameters like chemical composition or age. (19.79, 45.39) computed as an average of 65 Hipparcos mem- Recently, Chen & Zhao (1997) and Narayanan & Gould bers. They− explained the difference with the Hipparcos mean (1999) used purely geometrical methods to derive the distance parallax by small scale correlations between individual Hippar- of the Pleiades. Both methods are based on the hypothesis that cos parallaxes, greater than those described above. However, members share the same space velocity within a small random following their arguments, if the mean Hipparcos parallax is velocity dispersion of a few km s−1. biased, then the mean proper motion could also be biased. The Chen & Zhao (1997) used proper motions and radial veloc- fact that Narayanan & Gould use an average of the Hipparcos ities of members to derive the distance and the spatial velocity proper motions could be a problem since a variation of 1 mas/yr of the cluster with a global maximum likelihood procedure. in µδ, for instance, modifies the mean distance by about 2.5 pc. They obtained a distance of 135.56 0.72 pc. The tiny error bar In order to analyse the radial-velocity gradient method, a seems dubious. In addition, they used± the proper motions of new selection of radial velocity members was done. All the Hertzsprung (1947) which are only relative. The zero point of members with a CORAVEL radial velocity were considered. the proper motions is not given. From their resulting space ve- The spectroscopic binaries were rejected when they had no or- locity, the components of the proper motions (µα cos δ,µδ) can bital solution as well as all stars with less than 3 measurements be estimated to be (21.50, -33.04). The component in declina- (and which thus could also be non detected spectral binaries). tion is quite different from the Hipparcos mean proper motion 133 stars were selected on this basis. Their mean distance is of the cluster. Moreover, the differences between Hertzsprung’s 133.8 9.3 pc using the radial-velocity gradient method and the proper motions and the ACT catalogue proper motions (Urban mean± values of the centre, mean radial velocity and proper mo- et al. 1998) show very significant dependencies with magni- tion indicated in Tables 1 and 2 respectively. This distance con- tudes and coordinates. This suggests biases in the Herstzsprung firms the result of Narayanan & Gould (1999). However some catalogue of the order of few mas/yr. No discussion on proper- doubts can be casted upon the assumption that all the mem- motion biases, neither on the discrepant value of the mean proper bers share the same space velocity and are at the same distance. motion, is given by Chen & Zhao (1997). Adopting the same notations as Narayanan & Gould (1999), let 480 N. Robichon et al.: Open clusters with Hipparcos. I
Vr,i be the observed radial velocity of a member i, ni the unit Table 6. RMS normalized differences between cluster parallaxes and vector pointing in its line of sight and Vr, µ and n the mean Dambis photometric parallaxes as a function of number of Hipparcos radial velocity, mean proper motion and direction of the cluster stars in each cluster. center. Fig. 2 of Narayanan & Gould (1999) shows the differ- #of #of hσπi RMS ence between Vr,i Vr(n.ni) versus µ.ni. The slope of the linear regression of− these points gives directly the distance of members clusters (mas) the cluster. The most weighty points are then those with the most 2 28 1.03 1.00 extreme values of the proper-motion projection on the line of 3 11 0.80 1.25 sight, i.e. the most distant members from the cluster centre par- 4 12 0.60 1.26 allel to the proper motion direction. The cluster distance derived 5 4 0.55 0.98 6 6 0.48 1.57 selecting only the 27 stars satisfying µ.ni > 7 is 145 11 pc while it is 100 16 pc when using the| 106 other| members.± This ≥ 9 5 0.29 0.99 behaviour is quite± puzzling. If the CORAVELdata are free from any bias, this could indicate that the spatial structure of the clus- ter is not symmetrical or that the member velocity dispersion weight error (RMS error of the normalized differences) in sev- is not uniform, due to tidal distortion by the galactic potential eral groups of clusters containing the same number of Hipparcos for example. Nevertheless, investigations need to be carried out stars, have been computed (Table 6). If systematic errors were and would probably be the subject of a further paper. present, the RMS error should increase with the number of stars Summarizing this paragraph leads to two distance estimates in each cluster (since the mean formal error σπ decreases). for the Pleiades. The Hipparcos one around 120 pc (this paper No such trend has been found and the random errorsh i are mainly and van Leeuwen 1999) and a group of other values around responsible of the departure from the expected value (equal to 130 pc (PSSKH, O’Dell et al. 1994, Chen & Zhao 1997, and 1 if the formal parallax errors are realistic). The average unit- Narayanan & Gould 1999), part of them being compatible with weight error, 1.15, is not that bad since the membership in these the Hipparcos result within the error bars. distant clusters is not firmly determined. There is then no room for 1 mas systematic error or in only very few clusters. 4.2.2. Statistical properties of distant cluster mean parallaxes The estimation of the formal error of the mean parallax based on distant clusters seems statistically realistic. There is then no The MSF method may be used efficiently for distant (e.g. reason to suspect the presence of a problem on closer clusters, > 300 pc) clusters, since in this case, for a given absolute mag- because the error on the parallax is independent from the par- nitude error, the photometric parallax error becomes far smaller allax itself (Arenou et al. 1995). Concerning the Pleiades, this than the Hipparcos parallax error. Even a systematic absolute suggests that the formal parallax error has been correctly es- magnitude shift would only produce a slight asymmetry on the timated. The Pleiades could of course be at 4σ from the true distribution of differences between Hipparcos and MSF paral- parallax, but this is improbable, except if this is one special laxes; this may be seen when Hipparcos is compared to Loktin case where the small-scale correlations have been severely un- & Matkin (1994) distance moduli, in Arenou & Luri (1999). derestimated. Since these distant clusters are much more concentrated on No reason however has been found, which could justify this the sky than the nearby clusters, the effect of angular correlations hypothesis. For instance, one way of testing the way the small- should also be more obvious. If systematic errors were present scale correlations were taken into account is to study the vari- in the Hipparcos mean cluster parallaxes, then they would show ations of astrometric parameters with the angular distance be- up as either a systematic offset when cluster parallaxes are com- tween stars. Pleiades stars have been grouped in six bins of nine pared to photometric parallaxes, or as a scatter not accounted for stars with increasing distances from the centre and the mean in the formal errors. On the contrary, the errors on the normalized astrometric parameters for each bin are given in Table 7. All parallax differences appear normally distributed, the Gaussian values are compatible with the adopted mean values, and no (0,1) null hypothesis being compatible with the observations. significant trend appears for π or µα cos δ. Concerning µδ, the A further piece of evidence that the RGC correlations (and last bin (containing the 9 farthest stars from the cluster centre) consequently the formal error on the mean cluster parallaxes) is at 3.2 σ from the cluster mean value. If these 9 stars were seem to have been correctly taken into account is shown Table 6, rejected, the new mean values of the astrometric parameters re- where the mean parallaxes are compared with those deduced main compatible with the adopted values, but the last bin would from Dambis (1999). This reference was chosen because the then be at more than 2σ in µα cos δ and 4σ in µδ. formal error of the photometric parallaxes is indicated. There- No definitive explanation has been found to explain this be- fore, the statistical properties of mean cluster parallaxes may be haviour. However, if we add to this problem what has yet been safely studied. noticed about the radial velocities, and if the effect on parallaxes For the 66 clusters more distant than 300 pc, with at least two shown by Narayanan & Gould is not interpreted as systematics, members and a Dambis distance modulus, the normalized dif- there are indications that the spatial and/or kinematical distri- ferences between Hipparcos and Dambis parallaxes have been butions of the Pleiades are not as regular as expected. This is calculated. Then, the mean formal error σπ and the unit- h i possibly an explanation to the so-called Pleiades anomaly. N. Robichon et al.: Open clusters with Hipparcos. I 481
Table 7. Mean astrometric parameters on subsamples of the Pleiades (6 clusters have been compared to their photometric counterpart. bins of 9 stars) selected by increasing distances from the cluster centre. Using the 66 clusters more distant than 300 pc, the average dif- The average angular distance hdi from the cluster centre is indicated ference between cluster parallaxes, (Hipparcos Dambis), is indicated Table 8 in 7 quantiles of 9–10 clusters− according to π bin hdi πµα cos δ µδ the average ρ . Although some significant departures from ◦ α cos δ # mas mas/yr mas/yr 0 are present when individual stars are used (Arenou & Luri π 1 0.35 8.30 ± 0.46 19.73 ± 0.43 −44.87 ± 0.32 1999), the correlation ρα cos δ does not seem to influence the 2 0.67 9.07 ± 0.42 18.59 ± 0.42 −45.05 ± 0.32 mean cluster parallaxes. There is only one significant bin, at π 3 1.31 8.89 ± 0.45 19.35 ± 0.46 −45.59 ± 0.36 ρα cos δ 0.2, which is mainly due to one cluster, NGC 6231, 4 1.96 7.37 ± 0.58 18.97 ± 0.59 −45.58 ± 0.45 where all≈− stars have a negative parallax. The Pleiades being in 5 2.84 ...... π 8 65 ± 0 49 18 53 ± 0 51 −45 45 ± 0 41 the last bin, a 1 mas error due to ρα cos δ would be improbable. 6 4.24 8.17 ± 0.43 19.98 ± 0.51 −46.94 ± 0.38 all 1.90 8.46 ± 0.22 19.15 ± 0.23 −45.72 ± 0.18 4.3.2. Small scale effect: the Pleiades
Table 8. Errors on mean Hipparcos cluster parallax (mas) as a function PSSKH found a slope of 3.04 1.36 mas when computing a π ± π linear regression between ρ cos and π of their Pleiades mem- of the cluster average ρα cos δ. α δ bers. For the members determined in this study, a slope of 1.95 π 0.99 mas has been obtained. PSSKH interpreted this slope as hρα cos δihπHip − πDambisi the± signature of an Hipparcos systematic error. It should how- −0.34 −0.34 ± 0.32 ever be remembered that a correlation is not always a causality. −0.20 −0.53 ± 0.21 In the present case, the slope comes partially from the fact that 0.10 . . − 0 10 ± 0 32 the members in the central part of the cluster share the same −0.04 −0.29 ± 0.30 RGCs. This implies that the individual values of the parallax 0.03 0.17 ± 0.18 π 0.11 −0.04 ± 0.23 are correlated. This also implies that the ρα cos δ values are sim- 0.32 0.29 ± 0.31 ilar since the distribution of time on the parallactic ellipses are nearly the same. Due to the scanning law of the satellite in this area, the correlations are all around 0.3. But there are no rea- son for believing that an unbiased value of the mean parallax π 4.3. The effect of ρα cos δ π can be derived using ρα cos δ =0. Two kinds of Monte-Carlo According to PSSKH, systematic errors, on the order of 1 mas simulations have been done in order to assess these points. and thus far greater than the mean random error, are present First, using the assumed mean Hipparcos parallax and in the Hipparcos Catalogue. They would be due to the exist- proper motion (given in Table 2) of the Pleiades, simulated ing correlations between right ascension and parallax for stars abscissae have been generated, using the complete covariance within a small angular region. PSSKH have shown that there is matrix of these observations for the cluster. For each star, an π astrometric solution has been performed. For each simulated a trend in π vs ρ cos for the Pleiades, where the most lumi- α δ π π Pleiades, the ρ cos and π of each star member and a mean nous stars near the cluster centre, and with the highest ρα cos δ, α δ are those which raise the average parallax above that expected value of π derived from the intermediate data are computed. The π from MSF. In view of their results, PSSKH cautioned the users mean slope between ρα cos δ and π over the simulations spread π from -3.9 mas to 2.9 mas with a mean value 0.12 0.14 mas. of Hipparcos data for the stars with high ρα cos δ. The mean value of the mean parallaxes is 8.45− 0.25±mas. Keep- This section shows that, on the contrary, no bias on the par- ± π ing only the simulated Pleiades with a slope greater than 2 (less allax can be attributed to ρα cos δ neither on large scale nor on small scale. than 10% of the simulations), the mean parallax is 8.55 0.13 mas. This fully demonstrates that the weight of the stars± with a π large ρα cos δ do not bias the mean parallax value. 4.3.1. Behaviour over the whole sky π Secondly, the ρα cos δ correlation appears for a star if the Using the whole Hipparcos Catalogue, stars more distant than repartition of Hipparcos Reference Great Circles for this star is 500 pc according to their uvbyβ photometry have been selected. asymmetrical with regard to the position of the Sun (see chapter Taking into account this selection bias as described in Arenou 3.2 of the Hipparcos Catalogue 1997). In the case of Pleiades et al. (1995), Sect. 4, the zero-point of Hipparcos parallaxes is stars, the RGCs are splitted into two groups of 2.5 months over π the year, due to the scanning law of the satellite. The first group found to be 0.09 0.14 mas for 74 stars with ρα cos δ > 0.3, with an unit-weight− ± error of parallax 0.94 0.10, whereas the is centred on mid February and contains twice as many RGCs π± same computation with no restriction on ρ cos gives 0.05 as the second group which is centred on mid August. To reduce α δ π π − ± the ρ cos values, new reductions computing both individual 0.05 mas. Thus high ρα cos δ do not seem to play a special role α δ on the parallax of individual stars. and mean cluster astrometric parameters were carried out, while However, this does not exclude possible effects at small an- rejecting randomly half of the RGCs of the first group. As ex- π gular scales. For this purpose, the mean parallaxes for distant pected, the ρα cos δ values became equal to zero on the average 482 N. Robichon et al.: Open clusters with Hipparcos. I
( 0.01 0.02), but the mean parallax still remains quite the cluster sequences in the HR diagram, which will be studied in same− on± the average (8.40 0.12 mas), the slope between in- detail in a further paper. π ± dividual ρα cos δ and π remaining positive. A new selection of members, based on Hipparcos main Cat- One can conclude, from these two groups of simulations, alogue data, in the 9 clusters closer than 300 pc (except the that the mean values of the cluster parallax do not depend on Hyades) and in 9 rich clusters between 300 and 500 pc, has π the correlations ρα cos δ. been carried out. To these nearby clusters, a selection of 32 more distant clusters with at least 4 Hipparcos stars has also been added. 4.4. Other possible effects New mean astrometric parameters have been computed us- 4.4.1. Bad RGCs ing Hipparcos intermediate data, taking account of the star to star correlations. The precisions are better than 0.5 mas for par- For a normal RGC the individual precision on a star abscissa allaxes and 0.5 mas/yr for proper motions. For the most distant residual is 3 mas on average, the mean value being 0. If for some clusters the relative precision of the mean parallax is not as good reason bad RGCs had a large weight, the mean parallax could be but they may be used for statistical purposes. Proper motions, biased. For example, in the Pleiades, the mean parallaxes derived computed using the photometric parallaxes, may also be useful when removing all the abscissae of the RGC 221 or 1519 are, e.g. for the kinematical study of young stars. respectively, 8.24 0.23 and 8.56 0.23. These are the extreme Extensive tests have been applied, on distant clusters as well cases, for which a± convergence of± factors are responsible: the as on the Pleiades, which show that no obvious systematic errors large number of stars observed on these RGCs, the high value seem to be present in the obtained results, and that the computed of the partial derivative ∂a , the high parallactic factors at the ∂π precisions are representative of the true external errors. This time of observation and the good accuracy of the abscissae. should allow in turn to improve the MSF distance moduli and The influence of the other RGCs is, in most cases, smaller than to obtain reliable estimates of their external errors. 0.05 mas. Anyway, except perhaps RGC 674, which has a lot of outliers, there is no indication that any particular RGC should Acknowledgements. We thank Dr F. Mignard for his comments about be removed. And the mean astrometric parameters remain the the Pleiades Hipparcos data. We are grateful to Dr B. Miller for having same when discarding RGC 674. improved the style of the paper and to Dr T. de Zeeuw and J. de Bruijne for helpful comments. Extensive use has been made of the Simbad database, operated at CDS, Strasbourg, France, and of the Base Des 4.4.2. Binarity Amas (WEBDA). The possibility that systematic errors could originate from un- detected binarity has also been checked for the Pleiades case. Appendix A: hipparcos cluster members Apart from binary stars flagged as such by Hipparcos, and re- jected in the solutions given in the previous section, a solution The appendix lists the Hipparcos stars selected as members in has also been performed where all the ground-based (spectro- the nearby clusters. Table A1 contains the members seen as scopic or visual) binaries (20 stars) were rejected. The resulting multiple by Hipparcos and not used in the mean parameter cal- average parallax (8.50 0.26) is not significantly different from culation (H59 = C, O, G, V or X), while Table A2 gives the the adopted solution. ± numbers of single Hipparcos stars used. In fact, excluding the rare cases where the period of the bi- nary is about one year, no parallax bias due to unknown binarity References is expected. To assess this point, a simple test has been done: Arenou F., 1997, ESA SP-1200 vol.3, chap. 17 using the stars given in the orbital solutions of the Hipparcos Arenou F., Luri X., 1999, In: Egret D., Heck A. (eds.) Harmonizing DMSA/O annex, and computing a single star solution instead Cosmic Distance Scales in a Post-Hipparcos Era. ASP Conf. Series does not change significantly their parallax estimate. Since the Arenou F., Lindegren L., Frœschle´ M., et al., 1995, A&A 304, 52 binarity of these stars was known, undetected binaries (which Arenou F., Mignard F., Palasi J., 1997, ESA SP-1200 vol.3, chap. 20 implies a much smaller astrometric perturbation) are thus less Baumgardt H., 1998, A&A 340, 402 likely to produce a significant effect on the parallax. Brown A.G.A., Arenou F., van Leeuwen F., Lindegren L., Luri X., 1997, Hipparcos Venice’97, ESA SP-402, p. 63 Carrier F., Burki G., Richard C., 1998, A&A 341, 469 5. Conclusions Chen L., Zhao J.L., 1997, Chin. 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Table A1. Hipparcos cluster members flagged as multiple stars in HIP and not used for the calculation of the cluster mean astrometric parameters Cluster name H59 Hipparcos number Cluster name H59 Hipparcos number Coma Ber C 60525 NGC 6475 C 87218 87567 Pleiades C 17572 17923 V 87063 O 17694 17847 NGC 7092 C 106262 G 18559 G 106170 106409 IC 2391 C 42216 42715 NGC 2232 X 30076 IC 2602 C 52116 52171 52815 C 30535 53330 NGC 2516 C 38416 38416 38966 O 52419 39195 39562 X 51794 43044 Trumpler 10 C 43085 43087 43680 Praesepe C 42497 43688 G 42542 NGC 3532 C 54184 54809 NGC 2451 C 37322 NGC 2547 C 39479 α Per C 16244
Table A2. Hipparcos cluster members used for the calculation of the cluster mean astrometric parameters Cluster name Hipparcos number Coma Ber 59364 59399 59527 59833 59957 60025 60063 60066 60087 60123 60206 60266 60293 60304 60347 60351 60406 60458 60490 60582 60611 60649 60697 60746 60797 61071 61074 61147 61295 61402 Pleiades 16217 16407 16423 16635 16639 16753 16979 17000 17020 17034 17043 17044 17091 17125 17225 17245 17289 17316 17317 17325 17401 17481 17489 17497 17499 17511 17527 17531 17547 17552 17573 17579 17583 17588 17608 17625 17664 17692 17702 17704 17729 17776 17791 17851 17862 17892 17900 17999 18050 18091 18154 18431 18544 18955 IC 2391 42274 42374 42400 42450 42459 42504 42535 42702 42714 42726 43195 IC 2602 50102 50612 51131 51203 51300 51576 52059 52132 52160 52221 52261 52293 52328 52370 52502 52678 52701 52736 52867 53016 53913 53992 54168 Praesepe 41788 42106 42133 42164 42201 42247 42319 42327 42436 42485 42516 42518 42523 42549 42556 42578 42673 42705 42766 42952 42966 42974 42993 43050 43086 43199 NGC 2451 36653 37297 37450 37557 37623 37666 37697 37752 37829 37838 37982 38268 α Per 14697 14853 14949 14980 15040 15160 15259 15363 15388 15404 15420 15444 15499 15505 15531 15556 15654 15770 15819 15863 15878 15898 15911 15988 16011 16036 16047 16079 16118 16137 16147 16210 16318 16340 16403 16426 16430 16455 16470 16574 16625 16782 16826 16880 16966 16995 Blanco 1 163 212 232 257 328 349 389 395 477 512 585 653 77 NGC 6475 87102 87134 87230 87240 87360 87460 87472 87516 87529 87560 87580 87616 87624 87656 87671 87686 87698 87722 87785 87798 87844 88247 NGC 7092 105658 105659 105955 106270 106293 106297 106329 106848 NGC 2232 30197 30356 30595 30660 30700 30758 30761 30772 30789 31101 IC 4756 90958 90990 91171 91299 91312 91437 91513 91870 91909 NGC 2516 38226 38310 38433 38536 38739 38759 38783 38906 38994 39070 39073 39386 39438 39879 Trumpler 10 42477 42939 43055 43182 43209 43240 43285 43326 43450 NGC 3532 54147 54177 54197 54237 54266 54294 54306 54337 Collinder 140 35432 35641 35700 35761 35795 35822 35855 35905 36038 36045 36217 NGC 2547 39679 39759 39988 40011 40016 40024 40059 40336 40353 40385 40427 NGC 2422 36717 36773 36967 36981 37015 37018 37037 37047 37119 484 N. Robichon et al.: Open clusters with Hipparcos. I
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